Estimated generalized least squares in spatially misaligned regression models with Berkson error.

Area of Science:

• Environmental Science
• Geostatistics
• Statistical Modeling

Background:

• Spatial misalignment is common in environmental data, necessitating covariate prediction using methods like kriging.
• Kriging predictions introduce Berkson error into regression models, complicating covariance structure estimation.
• Estimating kriging parameters adds further uncertainty to the analysis.

Purpose of the Study:

• To characterize measurement error in spatially misaligned environmental data as a Berkson error model.
• To develop an estimated generalized least squares (EGLS) estimator that accounts for induced covariance structures.
• To provide guidance on when full accounting for covariance structures is critical.

Main Methods:

• Characterized total measurement error within a Berkson error model framework.
• Developed an EGLS estimator using estimated covariance parameters.
• Employed likelihood-based methods for estimating covariance parameters.
• Utilized simulation studies and real-world EPA data for validation.

Main Results:

• The proposed EGLS estimator effectively accounts for the complex error structure induced by kriging.
• Identified conditions under which fully addressing the covariance structure is crucial for accurate results.
• Demonstrated the practical application of the methodology with environmental data.

Conclusions:

• Accurate regression parameter estimation is achievable even with spatially misaligned environmental data and kriging-induced errors.
• The developed methods offer improved statistical rigor for environmental studies.
• The findings are applicable to various environmental monitoring and assessment programs.